Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Game {
	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] input = br.readLine().split(" ");
		int n = Integer.parseInt(input[0]);
		int m = Integer.parseInt(input[1]);
		int[][] grid = new int[n][m];
		int minVal = Integer.MAX_VALUE;
		for (int i = 0; i < n; i++) {
			String[] line = br.readLine().split(" ");
			for (int j = 0; j < m; j++) {
				int val = Integer.parseInt(line[j]);
				grid[i][j] = val;
				if (val < minVal) {
					minVal = val;
				}
			}
		}
		getMoves(grid, minVal);
	}

	private static void getMoves(int[][] grid, int minVal) {
		int moveCount = 0;
		StringBuilder solution = new StringBuilder();
		for (int i = 0; i < minVal; i++) {
			if (grid[0].length > grid.length) {
				for (int j = 0; j < grid.length; j++) {
					solution.append("row " + (j + 1) + "\n");
					moveCount++;
				}
			} else {
				for (int j = 0; j < grid[0].length; j++) {
					solution.append("col " + (j + 1) + "\n");
					moveCount++;
				}
			}
		}
		for (int j = 0; j < grid.length; j++) {
			for (int k = 0; k < grid[0].length; k++) {
				grid[j][k] -= minVal;
			}
		}
		int min = grid[0][0];
		for (int j = 1; j < grid[0].length; j++) {
			if (grid[0][j] < min) {
				min = grid[0][j];
			}
		}

		for (int j = 0; j < grid[0].length; j++) {
			int diff = grid[0][j] - min;
			for (int i = 0; i < diff; i++) {
				solution.append("col " + (j + 1) + "\n");
				moveCount++;
			}

			for (int i = 0; i < grid.length; i++) {
				grid[i][j] -= diff;
			}
		}

		for (int i = 0; i < grid.length; i++) {
			for (int j = 0; j < grid[0].length; j++) {
				if (grid[i][j] != grid[i][0]) {
					System.out.println(-1);
					return;
				}
			}
			for (int j = 0; j < grid[i][0]; j++) {
				solution.append("row " + (i + 1) + "\n");
				moveCount++;
			}

		}
		System.out.println(moveCount);
		System.out.println(solution);

	}

}